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Transactions of the American Mathematical Society

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Normal structure of the one-point stabilizer of a doubly-transitive permutation group. I


Author: Michael E. O’Nan
Journal: Trans. Amer. Math. Soc. 214 (1975), 1-42
MSC: Primary 20B20
DOI: https://doi.org/10.1090/S0002-9947-1975-0393207-3
MathSciNet review: 0393207
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Abstract: Let G be a doubly-transitive permutation group on a finite set X and x a point of X. Let $ {N^x}$ be a normal subgroup of $ {G_x}$, the subgroup fixing x, such that $ {N^x}$ is a T.I. set and not semiregular on $ X - x$. Then, $ PSL(n,q) \subseteq G \subseteq P\Gamma L(n,q)$. Geometrical consequences of this result are also obtained.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0393207-3
Article copyright: © Copyright 1975 American Mathematical Society